feat!: upgrade next, react and react-dom, move react/next dependency checker from payload to next package (#8323)

Fixes https://github.com/payloadcms/payload/issues/8013

**BREAKING:**
- Upgrades minimum supported @types/react version from
npm:types-react@19.0.0-rc.0 to npm:types-react@19.0.0-rc.1
- Upgrades minimum supported @types/react-dom version from
npm:types-react-dom@19.0.0-rc.0 to npm:types-react-dom@19.0.0-rc.1
- Upgrades minimum supported react and react-dom version from
19.0.0-rc-06d0b89e-20240801 to 19.0.0-rc-5dcb0097-20240918
- Upgrades minimum supported Next.js version from 15.0.0-canary.104 to
15.0.0-canary.160

---------

Co-authored-by: PatrikKozak <patrik@payloadcms.com>
Co-authored-by: Jacob Fletcher <jacobsfletch@gmail.com>

packages/plugin-search/package.json

@@ -56,14 +56,14 @@
   "devDependencies": {
     "@payloadcms/eslint-config": "workspace:*",
     "@types/express": "^4.17.9",
-    "@types/react": "npm:types-react@19.0.0-rc.0",
-    "@types/react-dom": "npm:types-react-dom@19.0.0-rc.0",
+    "@types/react": "npm:types-react@19.0.0-rc.1",
+    "@types/react-dom": "npm:types-react-dom@19.0.0-rc.1",
     "payload": "workspace:*"
   },
   "peerDependencies": {
     "payload": "workspace:*",
-    "react": "^19.0.0 || ^19.0.0-rc-06d0b89e-20240801",
-    "react-dom": "^19.0.0 || ^19.0.0-rc-06d0b89e-20240801"
+    "react": "^19.0.0 || ^19.0.0-rc-5dcb0097-20240918",
+    "react-dom": "^19.0.0 || ^19.0.0-rc-5dcb0097-20240918"
   },
   "publishConfig": {
     "exports": {
@@ -89,7 +89,7 @@
   },
   "homepage:": "https://payloadcms.com",
   "overrides": {
-    "@types/react": "npm:types-react@19.0.0-rc.0",
-    "@types/react-dom": "npm:types-react-dom@19.0.0-rc.0"
+    "@types/react": "npm:types-react@19.0.0-rc.1",
+    "@types/react-dom": "npm:types-react-dom@19.0.0-rc.1"
   }
 }